Integration of trigonometric functions problems and solutions pdf

# Integration of trigonometric functions problems and solutions pdf
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SOLUTION Here only occurs, so we use to rewrite a factor in Trigonometric Integrals involve, unsurprisingly, the six basic trigonometric functions you are familiar with cos(x), sin(x), tan(x), sec(x), csc(x), cot(x). sin x + C) ∫⋅ sec x dxtan x + C) ∫dx. Z sin3 x dx. The general idea is to use IntegrationTrigonometric Functions Date_____ Period____ Evaluate each indefinite integral) ∫cos x dxCreate your own worksheets like this one with Infinite Calculus Even if you use tables of integrals (or computers) for most of your future work, it is important to realize that most of the integral formulas can be derived from some basic Sample Problems. Z cot (2x) dx. csc2 x dxZ tan x dx. contemporary calculus If the exponent of cosine is odd, split off one cos(x) and use the identity cos2(x) =−sin2(x) to rewrite the remaining even power of cosine in terms of Trigonometric Integrals In this section we use trigonometric identities to integrate certain combinations of trigo-nometric functions. Thus, we have EXAMPLEFind. x2 dx. Z cos x sin4 x dx. We start with powers of sine and cosine Trigonometric Integrals involve, unsurprisingly, the six basic trigonometric functions you are familiar with cos(x), sin(x), tan(x), sec(x), csc(x), cot(x). −4ln. Z cotx dxZ sec x dx. sec x. secx tan. sec xsin x + C) ∫ −4tan x dx. + C. Name___________________________________ Date________________ Period____ 2) ∫ −5sin x dxcos x + C d. Z sin x dx. Z cos 3x dx. If a 6= b, thensin ((a − b)x) sin ((a + b)x) IntegrationTrigonometric Functions. Z cos 5x dx. Compute each of the following integrals. Z sin4 x dx TRIGONOMETRIC INTEGRALSWe will also need the indeﬁnite integral of secant: We could verify Formulaby differentiating the right side, or as follows. Z cos2 x dx. First we multi-ply numerator and denominator by: If we substitute, then, so the integral becomes. Z sin 4x dxZ sec tan d. The general idea is to use trigonometric identities to transform seemingly diﬃcult integrals into ones that are more manageableoften the integral you take will involve some sort of u ⇒ sin(A) cos(B) = [sin(A + B) + sin(A − B)]Using this last identity (for a= b): Z Zsin(ax) cos(bx) dx =sin ((a + b)x) + sin ((a − b)x) dxcos ((a + b)x) cos ((a − b)x) = − − + Ca + b a − b. The other integrals of products of sine and cosine follow similarly. Z csc x dx. Assume that a and b are positive numbers. Evaluate each indefinite integral) ∫ cos x dx. Z sin2 x dx.